The lawsuit filed Wednesday in Washington, D.C., accuses Cohen of smearing Moore's name and intentionally inflicting emotional distress.
In the disputed sketch, Baron Cohen, disguised as a purported Israeli anti-terrorism expert Erran Morad, demonstrated what he said was a device for detecting pedophiles, which beeped when it came into Moore's range. The suit claims defamation, intentional inflection of emotional distress and fraud.
They allege that "Defendant Cohen, while in character, falsely and fraudulently induces unsuspecting victims, like unsuspecting Judge Moore to be interviewed under dishonest, unethical, illegal and false pretenses, for his works".
The lawsuit asks for $95 million in punitive and compensatory damages.
After Moore discovered the truth, his attorney sent warnings to Cohen, Showtime and CBS that he would "resort to appropriate legal remedies if they chose to air the segment", according to the complaint.
Representatives for Baron Cohen have not responded to the lawsuit, filed in a federal court in Washington.
Showtime has not been served with the complaint, a spokesperson told ABC News, declining to comment further on the pending litigation.
The wand device remained silent as Cohen passed it over himself, but it beeped after he passed it over Moore several times.
Moore then says, "Maybe Israeli technology hasn't been developed properly", shaking Cohen's hand and ending the interview. "I've never had such an accusation of things".
Roy Moore said he was duped into appearing on the show and was "falsely portrayed as a sex offender and paedophile". "When the false, fraudulent and defamatory nature of the interview became apparent, Judge Moore terminated it".
During his campaign for Senate, Moore was accused by multiple women of sexual misconduct, including one allegation that he sexually assaulted a 14-year-old girl when he was in his 30s in 1979.
Mr Moore, 71, stood as a Republican candidate in last year's Senate race in his home state of Alabama, but lost to Democratic opponent Doug Jones.